Gaming machines currently exist with mechanical or video reels having symbols thereon and bonus schemes in which a player has one or more opportunities to select one or more symbols from a group of symbols to receive credits or bonus values. Such gaming devices which enable players to select symbols from a group of symbols are well known. Since players are seeking more entertainment and enjoyment, it is desirable to provide players with new gaming devices with new bonus schemes, enabling players to win larger payouts while simultaneously entertaining the players.